FIG. 1 is an example illustrating a multi-input, multi-output (MIMO) system according to the related art. As illustrated in FIG. 1, in operation, the receiving end uses a channel matrix H to determine a precoding matrix W and transmits (or feeds back) the determined preceding matrix to the transmitting end. At the same time, the transmitting end and the receiving end both possesses a set of matrices, one of which matches or is most similar to the determined precoding matrix W. Thereafter, the receiving end transmits (or feeds back) the index of the matrix which matches or is most analogous to the determined preceding matrix W. Here, the set of indexes corresponding to each of the analogous matrices are referred to as a codebook.
If the transmitting end and the receiving end use the shared codebook to feed back the index corresponding to the W matrix, the W matrix is determined based on the number of transmitting and receiving antennas. Subsequently, if the number of transmitting and receiving antennas increases, the number of W, which comprises the codebook, increases exponentially. In other words, the value of W is not fed back to the transmitting end, and rather, it is the index of the W value most similar or analogous to the actual W value which is fed back. As such, even a small increase in the number of antennas relates to a large increase in the number of W values in the codebook.
For example, if W matrix is a 2×2 matrix, the W matrix includes 4 elements. Therefore, even if there are 8 matrices included in the codebook comprises of these combinations, it is not difficult to find a matrix most similar to the actual W matrix. Furthermore, the performance drop is not significant.
In addition, if W matrix is a 4×4 matrix, for example, there are 16 elements in the W matrix. If there are only 8 matrices, as is the case with the 2×2 matrix, and if the W matrix most analogous to the actual W matrix is selected, there would be much difference between the actual W matrix and the W matrix selected from the codebook. Furthermore, if the index of the W matrix is transmitted to the transmitting end, the transmitting end receives the W matrix which is much different from the actual W matrix. Consequently, the performance could suffer. Furthermore, if the W matrix is a 4×4 matrix, there should be at least 64 matrices in the codebook to minimize performance drop.
Here, the number of bits transmitted from the transmitting end not only changes according to the number of antennas, but also has to have a storage (memory) which should be able to store more than 64 matrices, making it inefficient. At the same time, because the number of reserve W matrices increase exponentially with the increase of the transmitting and receiving antennas, it is difficult to prepare for subsequent increase in number of antennas.